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Simplifying 5(6z + -1) + -4(z + 5) = 18(z + 1) Reorder the terms: 5(-1 + 6z) + -4(z + 5) = 18(z + 1) (-1 * 5 + 6z * 5) + -4(z + 5) = 18(z + 1) (-5 + 30z) + -4(z + 5) = 18(z + 1) Reorder the terms: -5 + 30z + -4(5 + z) = 18(z + 1) -5 + 30z + (5 * -4 + z * -4) = 18(z + 1) -5 + 30z + (-20 + -4z) = 18(z + 1) Reorder the terms: -5 + -20 + 30z + -4z = 18(z + 1) Combine like terms: -5 + -20 = -25 -25 + 30z + -4z = 18(z + 1) Combine like terms: 30z + -4z = 26z -25 + 26z = 18(z + 1) Reorder the terms: -25 + 26z = 18(1 + z) -25 + 26z = (1 * 18 + z * 18) -25 + 26z = (18 + 18z) Solving -25 + 26z = 18 + 18z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-18z' to each side of the equation. -25 + 26z + -18z = 18 + 18z + -18z Combine like terms: 26z + -18z = 8z -25 + 8z = 18 + 18z + -18z Combine like terms: 18z + -18z = 0 -25 + 8z = 18 + 0 -25 + 8z = 18 Add '25' to each side of the equation. -25 + 25 + 8z = 18 + 25 Combine like terms: -25 + 25 = 0 0 + 8z = 18 + 25 8z = 18 + 25 Combine like terms: 18 + 25 = 43 8z = 43 Divide each side by '8'. z = 5.375 Simplifying z = 5.375
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